Space-time adaptive processing (STAP) is frequently used in radar systems to detect a target. STAP has been known since the early 1970's. In airborne radar systems, STAP improves target detection when interference in an environment, e.g., ground clutter and jamming, is a problem. STAP can achieve order-of-magnitude sensitivity improvements in target detection.
Typically, STAP involves a two-dimensional filtering technique applied to signals acquired by a phased-array antenna with multiple spatial channels. Coupling the multiple spatial channels with time dependent pulse-Doppler waveforms leads to STAP. By applying statistics of interference of the environment, a space-time adaptive weight vector is formed. Then, the weight vector is applied to the coherent signals received by the radar to detect the target.
FIG. 1 shows the signal model of the conventional STAP. When no target is detected, acquired signals 101 include a test signal x0 110 consisting of the disturbance d0 111 only, and a set of training signals xk, k=1, 2, . . . , K, 120, which are independent and identically distributed (i.i.d.) with the disturbance d0 111. When a target is detected, acquired signals 102 include the test signal 110 consisting of a target signal and the disturbance d0 111, and a set of i.i.d. training signals xk 120 with respect to d0 111. The target signal can be expressed as a product of a known steering vector s 130 and an unknown amplitude α.
As shown in FIG. 2 for conventional target detection with STAP, two types of the estimation sources of the disturbance covariance matrix are usually used for a homogeneous environment where the covariance matrix of the test signal 110 is the same as that of the training signal 120. These two methods are the estimation of disturbance covariance matrix 220 from training signals 120 via a covariance matrix estimator 210, and the generation of the disturbance covariance matrix 250 from prior knowledge 230 via a covariance matrix generator 240. The knowledge database can include maps of the environment, past measurements, etc.
As shown in FIG. 3, a conventional method, known as Kelly's generalized likelihood ratio test (GLRT), takes the acquired signals including the test signal 110 and training signals 120 as input, and then determines the ratio 330 of
                              max          α                ⁢                              max            R                    ⁢                                                    f                1                            ⁡                              (                                                      x                    0                                    ,                                      x                    1                                    ,                  …                  ⁢                                                                          ,                                                            x                      K                                        ❘                    α                                    ,                  R                                )                                      ⁢                                                  ⁢            and                                      310                                                max            R                    ⁢                                    f              0                        ⁡                          (                                                x                  0                                ,                                  x                  1                                ,                …                ⁢                                                                  ,                                                      x                    K                                    ❘                  R                                            )                                      ,                    320      
where α is the amplitude of the target signal, xk are target free training signals, x0 is the test signal, R is the covariance matrix of the training signals, and ƒ1( ) and ƒ0( ) are likelihood functions under two hypothesis H1, i.e., the target is present in the test signal, and H0, i.e., the target is not present in the test signal, respectively. The resulting test statistic 340 is compared to a threshold 350 to detect 360 the target.
FIG. 5 shows a conventional Bayesian treatment for the detection problem in a homogeneous environment, which assumes the disturbance covariance matrix is randomly distributed with some prior probability distribution.
Inputs are the test signal 110, the training signals 120 and a knowledge database 230. The resulting detectors are often referred to as the knowledge aided (KA) detectors for the homogeneous environment. The detector determines the ratio 530 of
                              max          α                ⁢                              ∫            R                    ⁢                                                    f                1                            ⁡                              (                                                      x                    0                                    ,                                      x                    1                                    ,                  …                  ⁢                                                                          ,                                                            x                      K                                        ❘                    α                                    ,                  R                                )                                      ⁢                          p              ⁡                              (                R                )                                      ⁢                                                  ⁢                          ⅆ              R                        ⁢                                                  ⁢            and                                      510                                    ∫          R                ⁢                                            f              0                        ⁡                          (                                                x                  0                                ,                                  x                  1                                ,                …                ⁢                                                                  ,                                                      x                    K                                    ❘                  R                                            )                                ⁢                      p            ⁡                          (              R              )                                ⁢                                          ⁢                                    ⅆ              R                        .                                      520      
The resulting test statistic T 540 is compared to a threshold 550 to detect 560 whether a target is present, or not.
For non-homogeneous environments, several models are known. One model is the well-known compound-Gaussian model, in which the training signal is a product of a scalar texture, and a Gaussian vector. The texture is used to simulate power oscillations among the signals.
Another model is the partially homogeneous environment, by which the training signals 120 share the covariance matrix with the test signal 110 up to an unknown scaling factor X.
FIG. 4 shows a conventional GLRT treatment on the detection problem, which results in the well-known adaptive coherence estimator (ACE) for the partially homogeneous environment. In that method, the input includes the acquired signals 101 comprising the test 110 and training signals 120. Then, the ratio 430 of
                                          max            α                    ⁢                                    max              λ                        ⁢                                          max                R                            ⁢                                                f                  1                                ⁡                                  (                                                            x                      0                                        ,                                          x                      1                                        ,                    …                    ⁢                                                                                  ,                                                                  x                        K                                            ❘                      α                                        ,                    λ                    ,                    R                                    )                                                                    ⁢                                  ,        and                    410                                    max          λ                ⁢                              max            R                    ⁢                                    f              0                        ⁡                          (                                                x                  0                                ,                                  x                  1                                ,                …                ⁢                                                                  ,                                                      x                    K                                    ❘                  λ                                ,                R                            )                                                  420      is determined, where α is amplitude of the test signal, xk are target free training signals, x0 is the test signal, R is the covariance matrix, ƒ1( ) and ƒ0( ) are the likelihood functions under two hypothesis H1, i.e., the target is present in the test signal, and H0, i.e., the target is not present in the test signal. The resulting test statistic 440 is compared to a threshold 450 to detect 460 the presence of a target.